Transonic aeroelastic solutions based upon the transonic small perturbation potential equation were studied. Time-marching transient solutions of plunging and pitching airfoils were analyzed using a complex exponential modal identification technique, and seven alternative integration techniques for the structural equations were evaluated. The HYTRAN2 code was used to determine transonic flutter boundaries versus Mach number and angle-of-attack for NACA 64A010 and MBB A-3 airfoils. In the code, a monotone differencing method, which eliminates leading edge expansion shocks, is used to solve the potential equation. When the effect of static pitching moment upon the angle-of-attack is included, the MBB A-3 airfoil can have multiple flutter speeds at a given Mach number.

/pdf/time-marching-transonic-flutter-solutions-including-angle-of-2d7gr7ddeb.pdf

Time-marching transonic flutter solutions including angle-of-attack effects

Aeroelastic time response analysis of thin airfoils by transonic code LTRAN2

A new approach to computational aeroelasticity

Transonic flutter analysis using the Euler equations

A method for predicting unsteady, subsonic aeroelastic responses was developed. The technique accounts for aerodynamic nonlinearities associated with angles of attack, vortex-dominated flow, static deformations, and unsteady behavior. The fluid and the wing together are treated as a single dynamical system, and the equations of motion for the structure and flow field are integrated simultaneously and interactively in the time domain. The method employs an iterative scheme based on a predictor-corrector technique. The aerodynamic loads are computed by the general unsteady vortex-lattice method and are determined simultaneously with the motion of the wing. Because the unsteady vortex-lattice method predicts the wake as part of the solution, the history of the motion is taken into account; hysteresis is predicted. Two models are used to demonstrate the technique: a rigid wing on an elastic support experiencing plunge and pitch about the elastic axis, and an elastic wing rigidly supported at the root chord experiencing spanwise bending and twisting. The method can be readily extended to account for structural nonlinearities and/or substitute aerodynamic load models. The time domain solution coupled with the unsteady vortex-lattice method provides the capability of graphically depicting wing and wake motion.

/pdf/numerical-model-of-unsteady-subsonic-aeroelastic-behavior-3afv3jtmkd.pdf

Numerical model of unsteady subsonic aeroelastic behavior

Flutter analyses are performed for a NACA 64A006 airfoil pitching and plunging in small-disturbance, unsteady transonic flow. Aerodynamic coefficients are obtained for M^ = 0.7, 0.8, 0.85, 0.8625, and 0.87, and for various values of low reduced frequencies. Two computer codes are used: 1) STRANS2 and UTRANS2 based upon the relaxation method and 2) LTRAN2 based upon the time-integration (indicial) method. Flutter results are presented as plots of flutter speed and corresponding reduced frequency vs one of the four parameters: airfoil/air mass density ratio, position of mass center, position of elastic axis, and freestream Mach number. In each figure, several sets of curves for different values of plunge/pitch frequency ratios are shown. The two sets of results based upon the two separate computer codes are, in general, in good agreement. For a special flutter analysis of a flat plate at M^ =0.7, the present methods agree well with the linear flat plate theory. The effect of each parameter on the trend of each curve of flutter speed is discussed in detail. The examples demonstrate the dip phenomenon of the curves for flutter speed in the transonic regime. Flutter results of transonic codes are compared with those obtained by linear flat plate theory.

Flutter analysis of a NACA 64A006 airfoil in small disturbance transonic flow

Transonic flutter analyses are performed for two conventional airfoils, NACA 64A006 and NACA 64A010, and three supercritical airfoils, MBB A-3, CAST 7, and the NASA TF-8A wing section at 65.3% semispan. Two degrees of freedom, plunging and pitching about the quarter-chord axis, are considered. The aerodynamic data are obtained by using the two transonic aerodynamics codes LTRAN2 (indicial and time integration methods) and STRANS2/UTRANS2 (harmonic analysis method). The unsteady aerodynamic data are computed within the low reduced frequency range. For all airfoils, the effect of Mach number on flutter speed is studied for several values of four different aeroelastic parameters. For the MBB A-3 supercritical airfoil, the effect of angle of attack on flutter speed is studied. For the cases of a flat plate and a NACA 64A006 airfoil, time response results are obtained by LTRAN2. Applicability and limitations of the two transonic codes are evaluated. Results for the transonic flutter characteristics of these airfoils are discussed and some comparisons are made. ah b,c

Application of Transonic Codes to Flutter Analysis of Conventional and Supercritical Airfoils

: Flutter analyses are performed for an NACA 64A006 and an NACA 64A010 airfoil by simultaneously using two transonic aerodynamic computational codes: (1) STRANS2 and UTRANS2 based on the relaxation method and (2) LTRAN2 based on the indicial and time-integration methods Flutter results are obtained as plots of flutter speeds and the corresponding reduced frequencies versus one of the four parameters; airfoil-air mass ratio; position of the mass center; position of the elastic axis; and free stream Mach number On each figure, several sets of curves for different values of plunge-to-pitch frequency ratios are shown simultaneously The flutter results obtained by using relaxation and the indicial methods are, in general, in good agreement The present flutter results for a special case of a thin parabolic airfoil at a low transonic Mach number of 07 compare favorably with that obtained by using linear flat plate theory The trend of each flutter curve and the effect of each parameter are discussed in detail

Flutter Analysis of Two-Dimensional and Two-Degree-of-Freedom Airfoils in Small-Disturbance, Unsteady Transonic Flow.

Application of transonic codes to flutter analysis of conventional and supercritical airfoils

: Flutter analysis is performed for a MBB A-3 supercritical airfoil at transonic Mach numbers. Two degrees of freedom, pitching and plunging, are considered. The unsteady aerodynamic data are obtained by using two separate transonic aerodynamic computational codes: (1) LTRAN2 based on the time integration method and (2) STRANS2 and UTRANS2 based on the harmonic analysis method. The steady aerodynamic results are shown in the form of upper and lower surface pressure curves. The unsteady aerodynamic coefficients are obtained and tabulated for various values of low reduced frequency by pitching the MBB A-3 airfoil about the quarter chord axis. For the case of zero mean angle of attack, the coefficients obtained by the two computer codes are directly compared and discussed. At design Mach number of 0.765 and zero mean angle of attack, flutter results are obtained by both methods and compared. They are presented as plots of flutter speed and the corresponding reduced frequency vs. one of the four parameters: airfoil - air mass ratio; position of mass center; position of elastic axis; and plunge-to-pitch frequency ratio.

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA084172&Location=U2&doc=GetTRDoc.pdf

P. Guruswamy

Papers

Flutter analysis of a NACA 64A006 airfoil in small disturbance transonic flow

Application of Transonic Codes to Flutter Analysis of Conventional and Supercritical Airfoils

Flutter Analysis of Two-Dimensional and Two-Degree-of-Freedom Airfoils in Small-Disturbance, Unsteady Transonic Flow.

Application of transonic codes to flutter analysis of conventional and supercritical airfoils

Flutter Analysis of a Two-Dimensional and Two-Degree-of-Freedom Supercritical Airfoil in Small-Disturbance Unsteady Transonic Flow.